ME 3701, Materials of Engineering Laboratory, LSU1

Experiment: Fatigue Testing

Objectives

- To demonstrate the use of the Instron servohydraulic testing machine for testing specimens subjected tocyclic (fatigue) loadings.

- To analytically approximate the fatigue damage accumulated in a part which is subjected to a known fatiguespectrum.

Introduction

A perusal of the broken parts in almost any scrap yard will reveal that the majority of failures occur at stressesbelow the yield strength. This is a result of the phenomenon called fatigue which has been estimated to beresponsible for up to 90% of the in-service part failures which occur in industry. If a bar of steel is repeatedlyloaded and unloaded at say 85% of its’ yield strength, it will ultimately fail in fatigue if it is loaded throughenough cycles. Also, even though steel ordinarily elongates approximately 30% in a typical tensile test,almost no elongation is evident in the appearance of fatigue fractures.

Basic fatigue testing involves the preparation of carefully polished test specimens (surface flaws are stressconcentrators) which are cycled to failure at various values of constant amplitude alternating stress levels.The data are condensed into an alternating Stress, S, verses Number of cycles to failure, N, curve which isgenerally referred to as a material’s S-N curve. As one would expect, the curves clearly show that a lownumber of cycles are needed to cause fatigue failures at high stress levels while low stress levels can resultin sudden, unexpected failures after a large number of cycles.

Background

Definition: Fatigue is the condition whereby a material cracks or fails as a result of repeated (cyclic) stressesapplied below the ultimate strength of the material.

Fatigue failures generally involve three stages:

1.) Crack Initiation,

2.) Crack Propagation, and

3.) Fast Fracture

Fatigue failures often occur quite suddenly with catastrophic (disastrous) results and although most insidiousfor metals, polymers and ceramics (except for glasses) are also susceptible to sudden fatigue failures.Fatigue causes brittlelike failures even in normally ductile materials with little gross plastic deformationoccurring prior to fracture. The process occurs by the initiation and propagation of cracks and, ordinarily, thefracture surface is close to perpendicular to the direction of maximum tensile stress.

Applied stresses may be axial (tension-compression), flexural (bending) or torsional (twisting) in nature. Ingeneral there are three possible fluctuating stress-time modes possible. The simplest is completely reversedconstant amplitude where the alternating stress varies from a maximum tensile stress to a minimumcompressive stress of equal magnitude. The second type, termed repeated constant amplitude, occurswhen the maxima and minima are asymmetrical relative to the zero stress level. Lastly, the stress level mayvary randomly in amplitude and frequency which is merely termed random cycling.

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Cyclic Stresses

Figure 1 Schematic Illustrating Cyclic Loading Parameters [Fuch & Stephens, 1980].

The following parameters are utilized to identify fluctuating stress cycles:

Mean Stress (σm): σm = 2minmax ss +

Stress Range (σr): σr = σmax - σmin

Stress Amplitude (σa): σa = 2minmax ss −

Stress Ratio (R): R = max

min

ss

Tensile stresses are normally considered positive and compressive stresses are considered negative.

The Fatigue Life (Nf) of a component is defined by the total number of stress cycles required to causefailure. Fatigue Life can be separated into three stages where

Nf = Ni + Np

1.) Crack Initiation (Ni) - Cycles required to initiate a crack. Generally results from dislocation pile-upsand/or imperfections such as surface scratches, voids, etc.

2.) Crack Growth (Np) - Cycles required to grow the crack in a stable manner to a critical size. Generallycontrolled by stress level. Since most common materials contain flaws, the prediction of crack growth is themost studied aspect of fatigue.

3.) Rapid Fracture - Very rapid critical crack growth occurs when the crack length reaches a critical value, ac.Since Rapid Fracture occurs quickly, there is no Rapid Fracture term in the Fatigue Life expression.

(S-Nf) Curve

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Most Fatigue Tests are conducted at what is referred to as “Constant Amplitude” which merely refers to thefact that the maximum and minimum stresses are constant for each cycle of a test. S-Nf refers to a plot ofConstant Amplitude Stress Level (S) verses Number of Cycles to Failure (Nf). S-Nf Curves are generallyplotted on semi-log or log-log paper where each dot represents the results of a single test specimen. Fatiguetests tend to be time consuming and expensive; each data point represents many hours of testing.

A prediction of failure for various stress levels can be made by studying a material’s S-Nf curve. The mosimportant part of the curve is often the portion to the right of the bend (or “knee”) in the curve that identifieswhat is termed the Endurance Limit or the Fatigue Limit. The Endurance Limit defines the stress level below

which the material will theoretically withstand an infinite number (~108) of stress cycles without fracture.

Fatigue Testing

Materials Testing to obtain S-Nf Curves is common; several ASTM standards address stress-based fatiguetesting. The "Rotating Bending Testing Machine" is similar to the original railroad axle-type Wohler usedwhere the bending moment is constant along the beam length. Each point on the Surface of the Rotating

Bend Specimen is subjected to fully-reversed cycling (σm = 0) and the tests are generally ConstantAmplitude.

Figure 3 Rotating Bending Testing Machine [Callister, 1994].

Figure 2 Stress Amplitude versus Numberof Cycles to Failure Curves [Flinn & Trojan,1990].

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"Reciprocating Bending Testing Machines" utilize a rotating crank to achieve a non-zero mean stressthrough positioning of the specimen with respect to the motor as shown in Figure 4.

Figure 4- Reciprocating Bending Testing Machine [Collins, 1981].

Similar to the Reciprocating Bending set-up, the "Direct Force Fatigue Testing Machines" apply axial loads asis illustrated in Figure 5.

Figure 5- Direct-Force Fatigue Testing Machine [Collins, 1981].

None-the-less, computer controlled "Servohydraulic Systems" are the most common in operation today; thenewest Instron Machine at LSU-ME is of this type. Computerized Servohydraulics are capable of bothMonitoring and Controlling a desired cyclic pattern in any of the following:

Load-Time Strain-Time Displacement-Time

This level of control allows the operator to program real-time fatigue spectrums including underloads andoverloads.

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"Component Testing" and/or "Full-Scale Prototype Tests" are still carried out on Fatigue-Critical structures.Most fatigue testing is conducted at the basic material level; differences between laboratory and serviceconditions must be considered by mechanical designers. Common test specimen types for obtaining fatiguedata are shown in Figure 6.

Figure 6 Fatigue Test Specimens: (a) Rotating Bending, (b) Cantilever Flat Sheet (cont.)

Figure 6 Fatigue Test Specimens: (c) buttoned axial dog-bone, (d) threaded axial dog-bone, (e) torsion, (f) combined stress, (g) axialcracked sheet, (h) part-through crack,(i) Compact tension and (j) three point bend specimen [Fuch & Stephens, 1980].

Fatigue Testing Procedures

A number of fatigue testing procedures have been developed to satisfy specific objectives:- Life distribution at a constant stress level.- Strength distribution at a constant life.

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- Design data at a minimal cost and time, etc.

The specific procedure followed should be carefully chosen based on the data requirements. The "StandardMethod" of fatigue testing is the most common and is utilized when only a few test specimens are available.A low number of tests (1 to 3) are conducted at a set of stress amplitudes that span the expected stress

range of the material; σa and Nf are recorded for each specimen. Run-Outs (specimens which do not fail

after 108 cycles) are noted (o−−>, see Figure 7) and rerun at a higher stress level to maximize the dataobtained from the limited specimen set.

Two S-Nf Curves are generally constructed: (1) an "Eyeballed Mean Curve" which passes near the mean ofeach tested stress amplitude, and (2) an "Eyeballed Conservative Curve" which is slightly below all of thedata points. Note that Probability Estimates for this method would be unreliable due to the scarcity of data"

Figure 7 Standard Method S-Nf Curves [Fuch & Stephens, 1980]

Analysis Method

Realize that most fatigue is NOT actually constant amplitude, but methods have been developed for utilizingconstant amplitude S-Nf results to predict failure under varying load histories. This area of fatigue is referredto as “Cumulative Damage”.

The most basic cumulative damage approach, and the most often utilized, is referred to as Miner’s Law whichis based on the man who developed the approach. Under this approach, the damage (D) caused by onecycle is merely defined as

D =1 Nf

Figure 8 Sample Actual Fatigue Spectrums[Fuch & Stephens, 1980].

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The damage produced by "n" cycles at a given stress level is given by

D = n Nf

Thus the cumulative damage for a set of cycles over a range of stress levels can be expressed as

D = Di∑ = n i N fi∑

where ni represents the number of cycles at stress level “i” and Nfi represents the number of cycles that willcause failure at stress level “i”.

Procedure

This lab consists of an in-class demonstration of using a Universal Testing Machine (Instron) to conductfatigue tests, a single test on a dog-bone specimen, and a fatigue failure prediction problem applying Miner’sLaw.

1. Fatigue Demonstration: The lab TA will demonstrate the versatility of the Instron Machine forconducting fatigue tests by showing how waveform, amplitude and frequency can be easily varied inPosition Control (similar flexibility can be achieved in Load Control) without any specimen mounted onthe machine.

2. Fatigue Test: The lab TA will conduct a constant amplitude, tension-tension fatigue test on adogbone sample up to fracture. Measure the sample prior to testing and record its’ dimensions;document the testing parameters used (waveform, maximum & minimum load, frequency, etc.).

3. Miner's Law Problem - see Lab Requirements

Lab Requirements

This is an In-Class Lab; all student work must be submitted prior to leaving the lab session.

1. Present the test parameters (waveform, D, Smax, Smin, Sm, Sr, Sa, R, f) and test results (Nf) for thefatigue sample tested. Comment on the results of the test.

2. Problem (Miner's Law): The S-Nf curve shown on the next page is for a low-carbon steel. If anautomobile strut made of this steel is subjected to the stress spectrum listed below over a 4month period:

a. How much damage will the part accumulate in 2 years based on Miner’s Law?

b. What’s the expected life for the part?

1 Cycle at 55 ksi

35 Cycles at 45 ksi

147 Cycles at 35 ksi

21,271 Cycles at 25 ksi

1,920,174 Cycles at 15 ksi

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